Question

From the figure D is a point on BC and
Triangle ADB, triangle ADC have equal perimeters.
Find AD.
A) 48
B) 49
C) 50 D) 51 E) None​

Answer 1

Answer:

From triangle ABC

By using pythagorean theorem:-

$AB ^{2} + AC^{2} = BC^{2} \\ \sqrt{ {60}^{2} + {80}^{2}} = BC \\ BC = 100$

BD + CD = 100 -------(1)

Now, perimeters of Triangle ADB & ADC are equal

AC + AD + CD = AD + AB + BD

80 + CD = 60 + BD

BD - CD = 20 --------(2)

Add (1) & (2)

2BD = 120

BD = 60

Substitute in (1)

CD = 40